Open Up Resources Logo

Lesson 2 From Polygons to Circles Solidify Understanding

Ready

Calculate the perimeter and area for each figure.

1.

Composite shape with one rectangle sides 2.5 and 10, a square, and another rectangle.

perimeter:

area:

2.

Two concentric circles larger circle with diameter 10 and smaller circle with radius 4. ff

perimeter of green (both inside and outside):

area of green:

3.

Square with semi-circle attached to one side with diameter 30

perimeter:

area:

4.

3/4 Circle with radius 25 and Square placed in missing piece of 1/4 circle.

perimeter:

area:

5.

Composite figure of two rectangles.

perimeter:

area:

6.

Composite figure.

perimeter:

area:

Set

7.

A circle and several congruent squares with side lengths equal to the radius of the circle are shown. Use these squares to estimate how many squares it takes to fill in the area of the circle. State what you notice. (Try using tracing paper or create cutouts to make a good estimate.)

Circle and a graph with 5 squares of side length 3.

8.

Which polygon has an area and perimeter closest to the circle in which it is inscribed? Why?

Circle A,B,C,D,E, F with inscribed triangle, square, pentagon, hexagon, octagon, and decagon.

9.

Given that the radius of each circle in the previous problem is feet, find the area of each of the regular polygons inscribed in the circle. List each area in the table below, along with the measure of one angle for each polygon and the side length of each polygon. (One interior angle and one side length are given.)

Shape

One Interior Angle

Length of One Side

Area of Figure

Triangle

Square

Pentagon

Hexagon

Octagon

Decagon

Circle

10.

Explain how a circle can be cut into sectors and reconfigured to appear approximately as a polygon that could have its area calculated using a standard formula. (Use a diagram with your explanation.)

11.

Explain how a circle can be broken into several rings or interior circles that can be rearranged to appear approximately as a polygon that could have its area calculated using a standard formula. (Use a diagram with your explanation.)

Go

Use the given circle in the following problems to find the indicated measures:

  1. circumference of the entire circle

  2. the fractional part of the circle represented by the ratio of the central angle to

  3. the shortest arc length that is intercepted by the central angle

(The shortest arc length from to is called the minor arc. The long distance from to around the circle is called the major arc.)

12.

Circle B with inscribed angle CBA 151 degrees and radius 5 cm.

  1. circumference of circle:

  2. ratio of central angle to :

  3. the shortest arc length :

13.

Circle B with inscribed angle CBA 43 degrees and radius 2 m.

  1. circumference of circle:

  2. ratio of central angle to :

  3. the shortest arc length :

14.

Circle B with inscribed angle CBA 116 degrees and radius 8 yds.

  1. circumference of circle:

  2. ratio of central angle to :

  3. the shortest arc length :

15.

Circle B with inscribed angle CBA 28 degrees and radius 12 cm.

  1. circumference of circle:

  2. ratio of central angle to :

  3. the shortest arc length :